How is the variance of a binomial distribution computed?

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How is the variance of a binomial distribution computed?

The variance of a binomial distribution is computed using the formula np(1-p), where n represents the number of trials, and p is the probability of success on each trial. This formula arises from the properties of the binomial distribution, which describes the number of successes in n independent Bernoulli trials. To understand why this formula is applicable, consider that the variance measures the dispersion of the outcomes around the expected value. In the binomial scenario, each trial is independent, and the variance captures how the successes distribute over the number of trials and their respective probabilities. The components of the formula are significant: "np" gives the expected number of successes, and "1-p" yields the probability of failure. The product of these two components reflects the variability in the number of successes across trials. Other options, while related to statistics and distributions, do not directly yield the variance for a binomial distribution. They illustrate methods or concepts that apply in other contexts or distributions but fail to pertain specifically to the calculation of variance in this particular type of distribution.

The variance of a binomial distribution is computed using the formula np(1-p), where n represents the number of trials, and p is the probability of success on each trial. This formula arises from the properties of the binomial distribution, which describes the number of successes in n independent Bernoulli trials.

To understand why this formula is applicable, consider that the variance measures the dispersion of the outcomes around the expected value. In the binomial scenario, each trial is independent, and the variance captures how the successes distribute over the number of trials and their respective probabilities.

The components of the formula are significant: "np" gives the expected number of successes, and "1-p" yields the probability of failure. The product of these two components reflects the variability in the number of successes across trials.

Other options, while related to statistics and distributions, do not directly yield the variance for a binomial distribution. They illustrate methods or concepts that apply in other contexts or distributions but fail to pertain specifically to the calculation of variance in this particular type of distribution.

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